Simplify the expression. $(3a^{4}+4a^{3}+6a)(4a^{3}+4a^{2})$
Solution: First use the distributive property. $ 3 a^4 (4 a^3) + 3 a^4 (4 a^2) + 4 a^3 (4 a^3) + 4 a^3 (4 a^2) + 6 a (4 a^3) + 6 a (4 a^2) $ Simplify. $ 12a^{7} + 12a^{6} + 16a^{6} + 16a^{5} + 24a^{4} + 24a^{3} $ $12a^{7}+28a^{6}+16a^{5}+24a^{4}+24a^{3}$ Identify like terms. $ { 12a^{7}} {+ 12a^{6}} {+ 16a^{6}} {+ 16a^{5}} {+ 24a^{4}} {+ 24a^{3}} $ Add the coefficients. $ { 12a^{7}} {+ 28a^{6}} {+ 16a^{5}} {+ 24a^{4}} {+ 24a^{3}} $